The only time you need more than one of the possible meanings at a time is when you want to make a pun. When translating, you'd have to explain both meanings, ruining the fun, but it's not a real barrier to expressing the content.
Poetry is so often cultural, and deals why certain things like rhyme and meter which influences that. It can be translated easily - the hard part is trying to keep all the cultural connotations of a word and the structure of the poem.
